Structural Dynamics and Modal Testing

Abstract

This chapter analyzes the response of a structure subjected to deter-ministic excitations. Conventional topics in single-degree-of-freedom and multi-degree-of-freedom structures are covered, including free vibration, forced vibration due to harmonic excitation, periodic excitation, impulsive excitation and arbitrary excitation, and modal superposition. Basic concepts in experimental modal testing are discussed as a simple application of structural dynamics, including logarithmic decrement, half-power bandwidth, harmonic load test and impact hammer test. The state-space approach is introduced for analyzing general dynamical systems. The basic principles of numerical solution and Newmark integration schemes are introduced, which allow one to compute the structural response for a given time history of excitation. Keywords Structural dynamics Á Modal testing Á Logarithmic decrement Á Half-power bandwidth Á Newmark scheme Á Impact hammer test In this chapter we discuss the subject of 'structural dynamics', which studies the response (e.g., displacement, velocity) of a structure obeying Newton's law of motion. The focus is on oscillatory behavior, commonly known as 'vibration'. 'Resonance' plays an important role, where an excitation of oscillatory nature can generate significantly larger response if it varies at a pace near the 'natural fre-quency' of the structure. Just as a musical instrument can produce sounds at different pitches, a structure can have more than one natural frequency. Associated with each frequency there is a specific spatial vibration pattern, called 'mode shape'. Natural frequencies and mode shapes are determined by an 'eigenvalue equation' that depends on the stiffness and mass of the structure. Together with damping characteristics they completely determine the structural dynamic response under applied loads. For textbooks on structural dynamics, see, e.g., Meirovitch (1986), Clough and Penzien (1993) and Beards (1996). We first discuss the vibration response of a single-degree-freedom (SDOF) structure, i.e., with only one variable in the equation of motion. Different types of excitations are considered. Multi-degree-of-freedom (MDOF) structures are next